CN105973516A

CN105973516A - Pulsation thrust method for identification of solid rocket engine

Info

Publication number: CN105973516A
Application number: CN201510920734.6A
Authority: CN
Inventors: 王建民; 韩丽; 李海波; 韦冰峰; 肖健; 张忠; 刘振皓; 任方
Original assignee: China Academy of Launch Vehicle Technology CALT; Beijing Institute of Structure and Environment Engineering
Current assignee: China Academy of Launch Vehicle Technology CALT; Beijing Institute of Structure and Environment Engineering
Priority date: 2015-12-11
Filing date: 2015-12-11
Publication date: 2016-09-28
Anticipated expiration: 2035-12-11
Also published as: CN105973516B

Abstract

The invention discloses a method for identifying the pulsating thrust of a solid rocket motor. The method includes: obtaining the acceleration of the solid rocket motor within a preset time period, the acceleration being the acceleration in the time domain t; transforming the acceleration in the time domain t into the acceleration in the time domain τ to obtain the acceleration corresponding to the time domain τ, The solid rocket motor has a time-invariant characteristic in the time domain τ; a random function is generated by a digital method within a preset time period; the random function is transformed into a random function of the time domain τ; the acceleration of the time domain τ and the The random functions of the time domain τ are respectively Fourier transformed to obtain the acceleration of the time domain τ and the Fourier transform of the random functions of the time domain τ; according to the acceleration of the time domain τ and the acceleration of the time domain τ The Fourier transform of the random function is identified to obtain the power spectral density of the pulsating thrust of the solid rocket motor; and the pulsating thrust of the solid rocket motor is calculated according to the power spectral density.

Description

A method for identifying the pulsating thrust of a solid rocket motor

技术领域 technical field

本发明涉及结构动力学领域，具体地，涉及一种用于识别固体火箭发动机的脉动推力的方法。 The invention relates to the field of structural dynamics, in particular to a method for identifying the pulsating thrust of a solid rocket motor.

背景技术 Background technique

利用固体火箭发动机地面试车试验，从而识别得到固体火箭发动机的脉动推力一直是识别发动机外载荷的重要途径。目前，采用测量固体火箭发动机在试车时的响应，并获得响应的功率谱密度，再通过脉动推力到响应的传递关系获得脉动推力。然而，发动机在工作过程中药量不断减少，这使得脉动推力到响应的传递关系随时间不断变化，且响应为非稳态的，而目前采用的识别发动机脉动推力的方法通常基于时不变结构假定，即传递关系不随时间变化，且响应为稳态的，这就导致脉动推力识别误差较大。利用发动机在地面进行试车试验，从而识别得到发动机的脉动推力其本质是一个时变结构的参数识别问题。需要采用时变结构的识别方法。 It is always an important way to identify the external load of the solid rocket motor by using the ground test of the solid rocket motor to identify the pulsating thrust of the solid rocket motor. At present, the response of the solid rocket motor is measured during the test run, and the power spectral density of the response is obtained, and then the pulsating thrust is obtained through the transfer relationship between the pulsating thrust and the response. However, the amount of fuel in the engine is continuously reduced during the working process, which makes the transfer relationship between the pulsating thrust and the response change with time, and the response is unsteady, and the current methods for identifying the pulsating thrust of the engine are usually based on the assumption of a time-invariant structure , that is, the transfer relationship does not change with time, and the response is steady-state, which leads to a large error in the identification of pulsating thrust. Using the engine to carry out the test run on the ground, so as to identify the pulsating thrust of the engine, its essence is a parameter identification problem of time-varying structure. Recognition methods using time-varying structures are required.

目前，时变结构的参数辨识方法可以分为参数化方法和非参数化方法。其中，非参数化方法在系统建模过程中不使用结构参数随时间变化的表达关系，包括频域分析方法、时域方法、希尔伯特-黄变换(HHT)方法。由于非参数化方法在识别过程中不使用结构参数随时间变化的表达关系，因此，识别精度比较低，尤其对于快时变系统更是如此。参数化方法在识别过程中使用结构参数随时间变化的表达关系，FS-TARMA方法是一种基于时域的参数化方法，在建模过程中将时变结构参数表示为一系列基函数的线性组合，从而将时变问题转化为时不变问题进行辨识。虽然该方法可以利用结构随时间变化的表达关系，但处理过程比较复杂，且不如频域方法直观。 At present, the parameter identification methods of time-varying structures can be divided into parametric methods and non-parametric methods. Among them, non-parametric methods do not use the expression relationship of structural parameters changing with time in the process of system modeling, including frequency domain analysis methods, time domain methods, and Hilbert-Huang Transform (HHT) methods. Since the non-parametric method does not use the expression relationship of structural parameters changing with time in the identification process, the identification accuracy is relatively low, especially for fast time-varying systems. The parameterization method uses the expression relationship of structural parameters changing with time in the identification process. The FS-TARMA method is a parameterization method based on time domain. In the modeling process, the time-varying structural parameters are expressed as a series of linear basis functions. Combination, so as to transform the time-varying problem into a time-invariant problem for identification. Although this method can use the time-varying expression relationship of the structure, the processing process is more complicated and not as intuitive as the frequency domain method.

发明内容 Contents of the invention

本发明的目的是提供一种用于识别固体火箭发动机的脉动推力的方法。所述方法通过时间域变换，将时变问题转化为准时不变问题，再结合基于傅里叶变换的模态参数识别算法识别得到固体火箭发动机的脉动推力，不仅提高了固体火箭发动机的脉动推力的识别精度和稳健性，而且还提高了对识别误差的适应性。 The object of the present invention is to provide a method for identifying the pulsating thrust of a solid rocket motor. The method converts the time-varying problem into a punctual invariant problem through time-domain transformation, and then combines the modal parameter identification algorithm based on Fourier transform to identify the pulsating thrust of the solid rocket motor, which not only improves the pulsating thrust of the solid rocket motor The recognition accuracy and robustness are improved, and the adaptability to recognition errors is also improved.

为了实现上述目的，本发明提供一种用于识别固体火箭发动机的脉动推力的方法。所述方法包括：获取所述固体火箭发动机在预设时间段内的加速度，所述加速度为时间域t的加速度；将时间域t的加速度变换为时间域τ的加速度，得到对应时间域τ的加速度，所述固体火箭发动机对时间域τ具有时不变特性；在预设时间段内用数字方法生成随机函数；将所述随机函数变换为时间域τ的随机函数；将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换，得到所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换；根据所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换识别得到所述固体火箭发动机的脉动推力的功率谱密度；以及根据所述功率谱密度计算得到所述固体火箭发动机的脉动推力。 In order to achieve the above objects, the present invention provides a method for identifying the pulsating thrust of a solid rocket motor. The method includes: acquiring the acceleration of the solid rocket motor within a preset time period, the acceleration being the acceleration in the time domain t; transforming the acceleration in the time domain t into the acceleration in the time domain τ, and obtaining the acceleration corresponding to the time domain τ Acceleration, the solid rocket motor has a time-invariant characteristic to the time domain τ; a random function is generated with a digital method within a preset time period; the random function is transformed into a random function of the time domain τ; the time domain τ The acceleration of the time domain τ and the random function of the time domain τ carry out Fourier transform respectively, obtain the acceleration of the time domain τ and the Fourier transform of the random function of the time domain τ; according to the acceleration of the time domain τ and The Fourier transform identification of the random function of the time domain τ obtains the power spectral density of the pulsating thrust of the solid rocket motor; and calculates the pulsating thrust of the solid rocket motor according to the power spectral density.

其中，所述将时间域t的加速度变换为时间域τ的加速度，得到对应时间域τ的加速度，所述固体火箭发动机在时间域τ具有时不变特性，具体包括：根据公式将时间域t的加速度变换为时间域τ的加速度；以及根据公式计算得到对应时间域τ的加速度，其中，所述预设时间段为T≤t≤0，T表示开始时间，T＜0，对应时间域τ的时间段为r表示所述固体火箭发动机的质量变化速率，表示所述时间域t的加速度，表示所述固体火箭发动机在时间域t的速度，根据公式计算得到，表示对应时间域τ的加速度。 Wherein, the acceleration of the time domain t is transformed into the acceleration of the time domain τ to obtain the acceleration corresponding to the time domain τ, and the solid rocket motor has a time-invariant characteristic in the time domain τ, which specifically includes: according to the formula Transform the acceleration of the time domain t into the acceleration of the time domain τ; and according to the formula Calculate the acceleration corresponding to the time domain τ, wherein the preset time period is T≤t≤0, T represents the start time, T<0, and the time period corresponding to the time domain τ is r represents the mass change rate of the solid rocket motor, represents the acceleration in the time domain t, represents the speed of the solid rocket motor in the time domain t, According to the formula calculated, Indicates the acceleration corresponding to the time domain τ.

其中，所述将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换之前，所述方法还包括：根据所述对应时间域τ的时间段将所述时间段划分为n段，第i段记为其中，i表示常数，表示第i段的起始值，表示第i段的终止值。 Wherein, before performing Fourier transform on the acceleration in the time domain τ and the random function in the time domain τ respectively, the method further includes: according to the time period corresponding to the time domain τ Divide the time period into n segments, and the i-th segment is recorded as Among them, i represents a constant, Indicates the starting value of the i-th segment, Indicates the termination value of the i-th segment.

其中，所述将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换，得到所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换，具体包括：根据以下不等时间间隔离散的傅里叶变换公式将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换，得到所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换： Wherein, the acceleration of the time domain τ and the random function of the time domain τ are respectively Fourier transformed to obtain the acceleration of the time domain τ and the Fourier transform of the random function of the time domain τ , specifically comprising: performing Fourier transform on the acceleration of the time domain τ and the random function of the time domain τ according to the following Fourier transform formulas separated by unequal time intervals to obtain the acceleration and the random function of the time domain τ Fourier transform of the random function of the time domain τ:

$T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) z z ((τ τ)) = = {Σ Σ}_{k k = = 00}^{N N - - 11} z z (({τ τ}_{k k}^{((i i))})) {e e}^{- - {jωτ jωτ}_{k k}} (({τ τ}_{k k + + 11}^{((i i))} - - {τ τ}_{k k}^{((i i))}))$

其中，表示函数z(τ)在第i段上的傅里叶变换，N表示大于1的正整数，k表示常数，表示函数在离散点处的取值，表示离散点，表示傅里叶变换因子。 in, Indicates that the function z(τ) in the i segment Fourier transform on , N represents a positive integer greater than 1, k represents a constant, Indicates that the function is at a discrete point value at represent discrete points, Represents the Fourier transform factor.

其中，根据所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换结果通过下式识别得到所述固体火箭发动机的脉动推力的功率谱密度： Wherein, according to the acceleration of the time domain τ and the Fourier transform result of the random function of the time domain τ, the power spectral density of the pulsating thrust of the solid rocket motor is obtained through the following equation identification:

$\frac{\sqrt{{P P}_{f f}}}{{m m}_{00}} \frac{11}{n no} {Σ Σ}_{i i = = 11}^{n no} \frac{11}{\sqrt{{((11 - - \frac{{\overset{&OverBar; &OverBar;}{ω ω}}^{22}}{{ω ω}^{22}}))}^{22} + + \frac{{((44 \overset{&OverBar; &OverBar;}{ξ ξ} \overset{&OverBar; &OverBar;}{ω ω} + + r r))}^{22}}{{ω ω}^{22} {(({rτ rτ}_{m m}^{((i i))} + + 22 \sqrt{11 + + r r T T}))}^{22}}}} = = A A ((ω ω))$

其中， $A (ω) = \frac{1}{n} Σ_{i = 1}^{n} \frac{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{y} (τ) |}{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) g (τ) |}, T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{y} (τ)$ 表示所述时间域τ的加速度在第i段上的傅里叶变换结果，表示所述时间域τ的随机函数g(τ)在第i段上的傅里叶变换结果，n表示正整数，A(ω)表示中间参数，m₀表示所述固体火箭发动机在开始时间的质量，P_f表示所述脉动推力的功率谱密度， $\overset{&OverBar;}{ω} = \sqrt{\frac{k}{m_{0}}}, \overset{&OverBar;}{ξ} = \frac{c}{2 m_{0} \overset{&OverBar;}{ω}}, τ_{m}^{(i)} = \frac{τ_{1}^{(i)} + τ_{2}^{(i)}}{2} .$ in, $A (ω) = \frac{1}{no} Σ_{i = 1}^{no} \frac{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{the y} (τ) |}{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) g (τ) |}, T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{the y} (τ)$ represents the acceleration of the time domain τ paragraph i The Fourier transform result on Represents the random function g(τ) of the time domain τ in the i-th segment The Fourier transform result on , n represents a positive integer, A(ω) represents an intermediate parameter, m ₀ represents the quality of the solid rocket motor at the start time, P _f represents the power spectral density of the pulsating thrust, $\overset{&OverBar;}{ω} = \sqrt{\frac{k}{m_{0}}}, \overset{&OverBar;}{ξ} = \frac{c}{2 m_{0} \overset{&OverBar;}{ω}}, τ_{m}^{(i)} = \frac{τ_{1}^{(i)} + τ_{2}^{(i)}}{2} .$

通过上述技术方案，变换时间域，将时变问题转化为准时不变问题，并根据时间域τ的加速度和时间域τ的随机函数的傅里叶变换识别得到固体火箭发动机的脉动推力的功率谱密度，再根据功率谱密度计算得到固体火箭发动机的脉动推力，不仅提高了固体火箭发动机的脉动推力的识别精度和稳健性，而且还提高了对识别误差的适应性，为固体火箭发动机的载荷识别提供了有力支撑。 Through the above technical scheme, transform the time domain, transform the time-varying problem into a punctual invariant problem, and obtain the power spectrum of the pulsating thrust of the solid rocket motor according to the Fourier transform of the acceleration in the time domain τ and the random function of the time domain τ Density, and then calculate the pulsating thrust of the solid rocket motor according to the power spectral density, which not only improves the identification accuracy and robustness of the pulsating thrust of the solid rocket Provided strong support.

附图说明 Description of drawings

图1是单自由度动力学系统的结构示意图； Fig. 1 is a structural schematic diagram of a single-degree-of-freedom dynamic system;

图2是本发明提供的用于识别固体火箭发动机的脉动推力的方法的流程图。 Fig. 2 is a flow chart of the method for identifying the pulsating thrust of the solid rocket motor provided by the present invention.

具体实施方式 detailed description

以下结合附图对本发明的具体实施方式进行详细说明。应当理解的是，此处所描述的具体实施方式仅用于说明和解释本发明，并不用于限制本发明。 Specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described here are only used to illustrate and explain the present invention, and are not intended to limit the present invention.

在介绍本发明提供的用于识别固体火箭发动机的脉动推力的方法之前，先详细描述一下本发明的推理过程。 Before introducing the method for identifying the pulsating thrust of the solid rocket motor provided by the present invention, the reasoning process of the present invention will be described in detail.

固体火箭发动机在地面进行试车试验是把固体火箭发动机固定在试车台上并进行点火工作。在试车试验全程通过测量固体火箭发动机结构上的加速度(振动响应)识别固体火箭发动机的脉动推力。在试车试验过程中，固体火箭发动机可以等效模拟为单自由度动力学系统。 The test run test of the solid rocket motor on the ground is to fix the solid rocket motor on the test bench and carry out the ignition work. The pulsating thrust of the solid rocket motor is identified by measuring the acceleration (vibration response) on the solid rocket motor structure throughout the test run. During the test run, the solid rocket motor can be equivalently simulated as a single-degree-of-freedom dynamic system.

图1是单自由度动力学系统的结构示意图。如图1所示，固体火箭发动机的质量随时间的变化关系可表示为m(t)＝m₀(1+rt)(1)，其中，m(t)表示固体火箭发动机的质量，m₀表示固体火箭发动机在开始时间(初始时刻)的质量，r表示固体火箭发动机的质量变化速率。 Figure 1 is a schematic diagram of the structure of a single-degree-of-freedom dynamic system. As shown in Figure 1, the relationship of the mass of the solid rocket motor with time can be expressed as m(t)=m ₀ (1+rt)(1), where m(t) represents the mass of the solid rocket motor, and m ₀ Indicates the mass of the solid rocket motor at the start time (initial moment), and r represents the mass change rate of the solid rocket motor.

该系统的动力学方程表示为： The kinetic equation of the system is expressed as:

$((11 + + r r t t)) \overset{\cdot\cdot \cdot\cdot}{x x} ((t t)) + + ((r r + + 22 \overset{&OverBar; &OverBar;}{ω ω} \overset{&OverBar; &OverBar;}{ξ ξ})) \overset{\cdot \cdot}{x x} ((t t)) + + {\overset{&OverBar; &OverBar;}{ω ω}}^{22} x x ((t t)) = = \frac{11}{{m m}_{00}} f f ((t t)) - - - - - - ((22))$

其中，均表示中间转化参数，k表示单自由度动力学系统的刚度，c表示单自由度动力学系统的黏滞阻尼系数，右端项f(t)表示固体火箭发动机的脉动推力，x(t)表示固体火箭发动机的位移，表示固体火箭发动机的速度，表示固体火箭发动机的加速度。 in, Both represent the intermediate conversion parameters, k represents the stiffness of the single-degree-of-freedom dynamic system, c represents the viscous damping coefficient of the single-degree-of-freedom dynamic system, the right-hand term f(t) represents the pulsating thrust of the solid rocket motor, and x(t) represents solid rocket motor displacement, represents the speed of the solid rocket motor, Indicates the acceleration of the solid rocket motor.

设(3)，其中，P_f表示固体火箭发动机的脉动推力的功率谱密度，e(t)表示根据随机数字生成算法随机生成的功率谱密度为1的随机函数。需要说明的是，固体火箭发动机的脉动推力的功率谱密度的特征与白噪声的功率谱密度的特征类似。 Assume (3), where P _f represents the power spectral density of the pulsating thrust of the solid rocket motor, and e(t) represents a random function with a power spectral density of 1 randomly generated according to the random number generation algorithm. It should be noted that the characteristics of the power spectral density of the pulsating thrust of the solid rocket motor are similar to those of the power spectral density of white noise.

将(3)式带入(2)式得到： Put (3) formula into (2) formula to get:

$((11 + + r r t t)) \overset{\cdot\cdot \cdot\cdot}{x x} ((t t)) + + ((r r + + 22 \overset{&OverBar; &OverBar;}{ω ω} \overset{&OverBar; &OverBar;}{ξ ξ})) \overset{\cdot \cdot}{x x} ((t t)) + + {\overset{&OverBar; &OverBar;}{ω ω}}^{22} x x ((t t)) = = \frac{\sqrt{{P P}_{f f}}}{{m m}_{00}} e e ((t t)) - - - - - - ((11))$

取预设时间段T≤t≤0进行考虑，T表示开始时间，其中T＜0，根据公式(2)将时间域t变换为时间域τ Take the preset time period T≤t≤0 for consideration, T represents the start time, where T<0, transform the time domain t into the time domain τ according to the formula (2)

$τ τ = = \frac{22}{r r} ((\sqrt{11 + + r r t t} - - \sqrt{11 + + r r T T})) - - - - - - ((33))$

对应时间域τ的时间段为 The time period corresponding to the time domain τ is

设变换后x(t)变换为y(τ)，e(t)变换为g(τ)，得到 Let x(t) be transformed into y(τ) and e(t) be transformed into g(τ) after transformation, we get

$\overset{\cdot &Center Dot;}{x x} ((t t)) = = \frac{11}{\sqrt{11 + + r r t t}} \overset{\cdot &Center Dot;}{y the y} ((τ τ)) - - - - - - ((44))$

$\overset{\cdot\cdot \cdot\cdot}{x x} ((t t)) = = - - \frac{r r}{22 ((11 + + r r t t)) \sqrt{11 + + r r t t}} \overset{\cdot &Center Dot;}{y the y} ((τ τ)) + + \frac{11}{11 + + r r t t} \overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ)) - - - - - - ((55))$

将式(4)、式(5)代入式(1)得到τ域表示的动力学方程为： Substituting Equation (4) and Equation (5) into Equation (1), the kinetic equation expressed in the τ domain is obtained as:

$\overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ)) + + \frac{44 \overset{&OverBar; &OverBar;}{ξ ξ} \overset{&OverBar; &OverBar;}{ω ω} + + r r}{r r τ τ + + 22 \sqrt{11 + + r r T T}} \overset{\cdot \cdot}{y the y} ((τ τ)) + + {\overset{&OverBar; &OverBar;}{ω ω}}^{22} y the y ((τ τ)) = = \frac{\sqrt{{P P}_{f f}}}{{m m}_{00}} g g ((τ τ)) - - - - - - ((66))$

将对应时间域τ的时间段划分为n段，第i段记为在对应时间域τ的时间段上对动力学方程(6)两边取傅里叶变换，假定在对应时间域τ的时间段上为不变的，可以取 will correspond to the time period of the time domain τ Divided into n segments, the i segment is recorded as Take the Fourier transform of both sides of the kinetic equation (6) in the time period corresponding to the time domain τ, assuming that in the time period corresponding to the time domain τ Invariant, you can take

$τ τ \approx \approx {τ τ}_{m m}^{((i i))} = = \frac{{τ τ}_{11}^{((i i))} + + {τ τ}_{22}^{((i i))}}{22},, ((i i = = 11,, 22,, ... ...,, n no)) - - - - - - ((77))$

则有 then there is

$\frac{T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) \overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ))}{T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) g g ((τ τ))} = = \frac{\sqrt{{P P}_{f f}}}{{m m}_{00} ((11 - - \frac{{\overset{&OverBar; &OverBar;}{ω ω}}^{22}}{{ω ω}^{22}} - - j j \frac{44 \overset{&OverBar; &OverBar;}{ξ ξ} \overset{&OverBar; &OverBar;}{ω ω} + + r r}{ω ω (({rτ rτ}_{m m}^{((i i))} + + 22 \sqrt{11 + + r r T T}))}))},, ((i i = = 11,, 22,, ... ...,, n no)) - - - - - - ((88))$

其中，表示时间域τ的加速度在时间段上的傅里叶变换，表示时间域τ的随机函数g(τ)在时间段上的傅里叶变换。对式(8)取模并对i平均得到 in, Indicates the acceleration in the time domain τ in time period Fourier transform on Represents the random function g(τ) in the time domain τ in the time period Fourier transform on . Take the modulus of formula (8) and average i to get

$\frac{\sqrt{{P P}_{f f}}}{{m m}_{00}} \frac{11}{n no} {Σ Σ}_{i i = = 11}^{n no} \frac{11}{\sqrt{{((11 - - \frac{{\overset{&OverBar; &OverBar;}{ω ω}}^{22}}{{ω ω}^{22}}))}^{22} + + \frac{{((44 \overset{&OverBar; &OverBar;}{ξ ξ} \overset{&OverBar; &OverBar;}{ω ω} + + r r))}^{22}}{{ω ω}^{22} {(({rτ rτ}_{m m}^{((i i))} + + 22 \sqrt{11 + + r r T T}))}^{22}}}} = = \frac{11}{n no} {Σ Σ}_{i i = = 11}^{n no} \frac{| | T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) \overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ)) | |}{| | T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) g g ((τ τ)) | |} - - - - - - ((99))$

设 Assume

$A A ((ω ω)) = = \frac{11}{n no} {Σ Σ}_{i i = = 11}^{n no} \frac{| | T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) \overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ)) | |}{| | T T ((ω ω,, {τ τ}_{11}^{((i i))},, {τ τ}_{22}^{((i i))})) g g ((τ τ)) | |} - - - - - - ((1010))$

则 but

$\frac{\sqrt{{P P}_{f f}}}{{m m}_{00}} \frac{11}{n no} {Σ Σ}_{i i = = 11}^{n no} \frac{11}{\sqrt{{((11 - - \frac{{\overset{&OverBar; &OverBar;}{ω ω}}^{22}}{{ω ω}^{22}}))}^{22} + + \frac{{((44 \overset{&OverBar; &OverBar;}{ξ ξ} \overset{&OverBar; &OverBar;}{ω ω} + + r r))}^{22}}{{ω ω}^{22} {(({rτ rτ}_{m m}^{((i i))} + + 22 \sqrt{11 + + r r T T}))}^{22}}}} = = A A ((ω ω)) - - - - - - ((1111))$

如果A(ω)已知，与白噪声激励下单自由时不变系统参数识别方法类似，可以通过式(11)识别出参数(或)、从而能够得到固体火箭发动机的脉动推力。其中，表示单自由度动力学系统在t＝0时刻的伪模态频率。 If A(ω) is known, similar to the identification method of single free time-invariant system parameters under white noise excitation, the parameters can be identified by formula (11) (or ), Thus, the pulsating thrust of the solid rocket motor can be obtained. in, Indicates the pseudo-modal frequency of the single-degree-of-freedom dynamical system at time t=0.

下面讨论如何获得A(ω)。由式(3)可得 How to obtain A(ω) is discussed below. From formula (3) can get

$\overset{\cdot\cdot \cdot\cdot}{y the y} ((τ τ)) = = ((11 + + r r t t)) \overset{\cdot\cdot \cdot\cdot}{x x} ((t t)) + + \frac{r r}{22} \overset{\cdot &Center Dot;}{x x} ((t t)) - - - - - - ((1212))$

可以通过安装在固体火箭发动机前端框上的加速度传感器直接测量得到，可以通过积分得到，因此，可以通过式(12)获得。g(τ)由e(t)经时间变换直接获得，而e(t)可以通过随机数字生成算法获得。至此，g(τ)均已知。但需要注意的是，因e(t)一般按等间隔t离散，经式(3)变换后g(τ)为不等间隔τ离散，因此在对g(τ)进行傅里叶变换时，需要采用不等时间间隔离散的傅里叶变换算法。不等时间间隔离散的傅里叶变换算法可以直接用傅里叶变换定义。任意函数z(τ)的傅里叶变换定义为 It can be directly measured by the acceleration sensor installed on the front frame of the solid rocket motor, able to pass Integral gets, therefore, It can be obtained by formula (12). g(τ) is directly obtained from e(t) through time transformation, and e(t) can be obtained through a random number generation algorithm. So far, g(τ) are known. But it should be noted that, because e(t) is generally discretized at equal intervals t, after transformation by formula (3) g(τ) is discretized with unequal interval τ, so for When performing Fourier transform on g(τ), it is necessary to use the Fourier transform algorithm with discrete time intervals. The discrete Fourier transform algorithm for unequal time intervals can be defined directly by Fourier transform. The Fourier transform of any function z(τ) is defined as

$T T ((ω ω,, {τ τ}_{11},, {τ τ}_{22})) z z ((τ τ)) = = {&Integral; &Integral;}_{{τ τ}_{11}}^{{τ τ}_{22}} z z ((τ τ)) {e e}^{- - j j ω ω τ τ} d d τ τ - - - - - - ((1313))$

将式(13)中的z(τ)在不等间隔τ进行离散，用离散点值进行积分得 Discretize z(τ) in formula (13) at unequal intervals τ, and integrate with discrete point values to get

$T T ((ω ω,, {τ τ}_{l l},, {τ τ}_{h h})) z z ((τ τ)) \approx \approx {Σ Σ}_{i i = = 00}^{N N - - 11} z z (({τ τ}_{i i})) {e e}^{- - {jωτ jωτ}_{i i}} (({τ τ}_{i i + + 11} - - {τ τ}_{i i})) - - - - - - ((1414))$

其中，τ_i(i＝0,1,…,N-1)为区间[τ_l,τ_h]的离散点，z(τ_i)表示在离散点τⁱ处的函数值。 Wherein, τ _i (i=0,1,...,N-1) is a discrete point in the interval [τ _l ,τ _h ], and z(τ _i ) represents the function value at the discrete point τ ⁱ .

至此，式(10)的右端均可以获得，从而A(ω)可以获得。这样通过白噪声激励下单自由度时不变系统参数识别方法即可识别出参数(或)、获得P_f，从而能够得到固体火箭发动机的脉动推力。 So far, the right end of formula (10) can be obtained, so A(ω) can be obtained. In this way, the parameter identification method of single degree of freedom time-invariant system under white noise excitation can identify the parameter (or ), Obtain P _f , so that the pulsating thrust of the solid rocket motor can be obtained.

图2是本发明提供的用于识别固体火箭发动机的脉动推力的方法的流程图。如图2所示，本发明提供的用于识别固体火箭发动机的脉动推力的方法包括：在步骤S101中，获取所述固体火箭发动机在预设时间段内的加速度，所述加速度为时间域t的加速度。具体地，获取所述固体火箭发动机在试车台进行试车试验时的预设时间段内的加速度。所述加速度由安装在固体火箭发动机前端框上的加速度传感器直接测量得到。其中，加速度传感器的安装方向为固体火箭发动机的纵向。更为具体地，在获取所述固体火箭发动机在预设时间段内的加速度之前，选取固体火箭发动机试车加速度测量的预设时间段。选取的方式为开始记录和结束记录之间尽量长的一段有效数据，计开始时间为T(T＜0)，结束时间为0，预设时间段为T≤t≤0。 Fig. 2 is a flow chart of the method for identifying the pulsating thrust of the solid rocket motor provided by the present invention. As shown in Figure 2, the method for identifying the pulsating thrust of a solid rocket motor provided by the present invention includes: in step S101, acquiring the acceleration of the solid rocket motor within a preset time period, the acceleration being the time domain t acceleration. Specifically, the acceleration of the solid rocket motor within a preset period of time when a test run test is performed on a test bench is acquired. The acceleration is directly measured by an acceleration sensor installed on the front frame of the solid rocket motor. Wherein, the installation direction of the acceleration sensor is the longitudinal direction of the solid rocket motor. More specifically, before acquiring the acceleration of the solid rocket motor within a preset time period, a preset time period for testing acceleration of the solid rocket motor is selected. The selected method is a period of valid data as long as possible between the start of recording and the end of recording, the counting start time is T (T<0), the end time is 0, and the preset time period is T≤t≤0.

接着，在步骤S102中，将时间域t的加速度变换为时间域τ的加速度，得到对应时间域τ的加速度，所述固体火箭发动机在时间域τ具有时不变特性。具体地，该步骤包括：根据公式将时间域t的加速度变换为时间域τ的加速度； Next, in step S102, the acceleration in the time domain t is transformed into the acceleration in the time domain τ to obtain the acceleration corresponding to the time domain τ, and the solid rocket motor has a time-invariant characteristic in the time domain τ. Specifically, this step includes: according to the formula Transform the acceleration of the time domain t into the acceleration of the time domain τ;

以及根据公式计算得到对应时间域τ的加速度，其中，所述预设时间段为T≤t≤0，T表示开始时间，T＜0，对应时间域τ的时间段为r表示所述固体火箭发动机的质量变化速率，表示所述时间域t的加速度，表示所述固体火箭发动机在时间域t的速度，根据公式计算得到，表示对应时间域τ的加速度。其中，所述时间域τ具有时不变特性指的是相关参数在时间域t是时变的，而经过时间域变换之后在时间域τ是时不变的。 and according to the formula Calculate the acceleration corresponding to the time domain τ, wherein the preset time period is T≤t≤0, T represents the start time, T<0, and the time period corresponding to the time domain τ is r represents the mass change rate of the solid rocket motor, represents the acceleration in the time domain t, represents the speed of the solid rocket motor in the time domain t, According to the formula calculated, Indicates the acceleration corresponding to the time domain τ. Wherein, the time-invariant characteristic of the time domain τ means that the relevant parameters are time-varying in the time domain t, but are time-invariant in the time domain τ after time-domain transformation.

紧接着，在步骤S103中，在预设时间段内用数字方法生成随机函数。在具体的应用中，根据随机数字生成算法在预设时间段内随机生成功率谱密度为1的随机函数。接着，在步骤S104中，将所述随机函数变换为时间域τ的随机函数g(τ)。 Next, in step S103, a random function is generated digitally within a preset period of time. In a specific application, a random function with a power spectral density of 1 is randomly generated within a preset time period according to a random number generation algorithm. Next, in step S104, the random function is transformed into a random function g(τ) in the time domain τ.

然后，在步骤S105中，将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换，得到所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换。具体地，所述将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换之前，根据所述对应时间域τ的时间段将所述时间段划分为n段，第i段记为其中，i表示常数，表示第i段的起始值，表示第i段的终止值。更为具体地，该步骤包括：根据以下不等时间间隔离散的傅里叶变换公式将所述时间域τ的加速度和所述时间域τ的随机函数分别进行傅里叶变换，得到所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换： Then, in step S105, the acceleration of the time domain τ and the random function of the time domain τ are respectively subjected to Fourier transform to obtain the Fourier transform of the acceleration of the time domain τ and the random function of the time domain τ Leaf transformation. Specifically, before performing Fourier transform on the acceleration in the time domain τ and the random function in the time domain τ, according to the time period corresponding to the time domain τ Divide the time period into n segments, and the i-th segment is recorded as Among them, i represents a constant, Indicates the starting value of the i-th segment, Indicates the termination value of the i-th segment. More specifically, this step includes: performing Fourier transform on the acceleration in the time domain τ and the random function in the time domain τ according to the following discrete Fourier transform formula with unequal time intervals to obtain the time The Fourier transform of the acceleration in the domain τ and the random function in the time domain τ:

接着，在步骤S106中，根据所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换识别得到所述固体火箭发动机的脉动推力的功率谱密度。具体地，该步骤包括：根据所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换通过下式识别得到所述固体火箭发动机的脉动推力的功率谱密度： Next, in step S106, the power spectral density of the pulsating thrust of the solid rocket motor is obtained according to the Fourier transform identification of the acceleration in the time domain τ and the random function of the time domain τ. Specifically, this step includes: according to the acceleration of the time domain τ and the Fourier transform of the random function of the time domain τ, the power spectral density of the pulsating thrust of the solid rocket motor is obtained through the following equation identification:

其中， $A (ω) = \frac{1}{n} Σ_{i = 1}^{n} \frac{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{y} (τ) |}{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) g (τ) |}, T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{y} (τ)$ 表示所述时间域τ的加速度在第i段上的傅里叶变换结果，表示所述时间域τ的随机函数g(τ)在第i段上的傅里叶变换结果，n表示正整数，A(ω)表示中间参数，m₀表示所述固体火箭发动机在开始时间的质量，P_f表示所述脉动推力的功率谱密度， $\overset{&OverBar;}{ω} = \sqrt{\frac{k}{m_{0}}}, \overset{&OverBar;}{ξ} = \frac{c}{2 m_{0} \overset{&OverBar;}{ω}}, τ_{m}^{(i)} = \frac{τ_{1}^{(i)} + τ_{2}^{(i)}}{2} .$ 更为具体地，根据所述时间域τ的加速度和所述时间域τ的随机函数的傅里叶变换利用基于傅里叶变换的模态参数识别算法识别得到所述固体火箭发动机的脉动推力的功率谱密度。 in, $A (ω) = \frac{1}{no} Σ_{i = 1}^{no} \frac{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{the y} (τ) |}{| T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) g (τ) |}, T (ω, τ_{1}^{(i)}, τ_{2}^{(i)}) \overset{\cdot\cdot}{the y} (τ)$ represents the acceleration of the time domain τ paragraph i The Fourier transform result on Represents the random function g(τ) of the time domain τ in the i-th segment The Fourier transform result on , n represents a positive integer, A(ω) represents an intermediate parameter, m ₀ represents the quality of the solid rocket motor at the start time, P _f represents the power spectral density of the pulsating thrust, $\overset{&OverBar;}{ω} = \sqrt{\frac{k}{m_{0}}}, \overset{&OverBar;}{ξ} = \frac{c}{2 m_{0} \overset{&OverBar;}{ω}}, τ_{m}^{(i)} = \frac{τ_{1}^{(i)} + τ_{2}^{(i)}}{2} .$ More specifically, according to the Fourier transform of the acceleration in the time domain τ and the random function of the time domain τ, the pulsating thrust of the solid rocket motor is obtained by using a Fourier transform-based modal parameter identification algorithm Power Spectral Density.

最后，在步骤S107中，根据所述功率谱密度计算得到所述固体火箭发动机的脉动推力。其中，具体的计算方法为本领域技术人员所公知的计算方法。 Finally, in step S107, the pulsating thrust of the solid rocket motor is calculated according to the power spectral density. Wherein, the specific calculation method is a calculation method known to those skilled in the art.

本发明提供的方法利用了发动机燃料质量随时间变化的关系，并通过时间域变换，将时变问题转化为准时不变问题，从而可采用传统的基于傅里叶变换的模态参数识别算法进行脉动推力识别。该方法既利用了时变结构对时间变化的关系信息，同时又有频域方法的简洁性与直观性。实际应用表明该方法对测量误差适应性极强，是一种理想的利用发动机地面试车试验识别发动机脉动推力的有效方法，解决了现有辨识方法不考虑发动机时变带来的问题，使识别的脉动推力更准确。 The method provided by the present invention utilizes the relationship of the engine fuel quality over time, and transforms the time-varying problem into a time-invariant problem through time-domain transformation, so that the traditional Fourier transform-based modal parameter identification algorithm can be used for Pulsating thrust identification. This method not only utilizes the relationship information of the time-varying structure to the time change, but also has the simplicity and intuitiveness of the frequency-domain method. Practical application shows that this method has strong adaptability to measurement errors, and it is an ideal and effective method to identify engine pulsating thrust by using the engine ground test test. Pulsating thrust is more accurate.

以上结合附图详细描述了本发明的优选实施方式，但是，本发明并不限于上述实施方式中的具体细节，在本发明的技术构思范围内，可以对本发明的技术方案进行多种简单变型，这些简单变型均属于本发明的保护范围。 The preferred embodiment of the present invention has been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the specific details of the above embodiment, within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, These simple modifications all belong to the protection scope of the present invention.

另外需要说明的是，在上述具体实施方式中所描述的各个具体技术特征，在不矛盾的情况下，可以通过任何合适的方式进行组合，为了避免不必要的重复，本发明对各种可能的组合方式不再另行说明。 In addition, it should be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable way if there is no contradiction. The combination method will not be described separately.

此外，本发明的各种不同的实施方式之间也可以进行任意组合，只要其不违背本发明的思想，其同样应当视为本发明所公开的内容。 In addition, various combinations of different embodiments of the present invention can also be combined arbitrarily, as long as they do not violate the idea of the present invention, they should also be regarded as the disclosed content of the present invention.

Claims

1. A method for identifying a pulsating thrust of a solid rocket engine, the method comprising:

acquiring the acceleration of the solid rocket engine in a preset time period, wherein the acceleration is the acceleration of a time domain t;

converting the acceleration of the time domain t into the acceleration of the time domain tau to obtain the acceleration corresponding to the time domain tau, wherein the solid rocket engine has a time-invariant characteristic in the time domain tau;

generating a random function by a digital method in a preset time period;

transforming the random function into a random function of a time domain τ;

respectively carrying out Fourier transformation on the acceleration of the time domain tau and the random function of the time domain tau to obtain the Fourier transformation of the acceleration of the time domain tau and the random function of the time domain tau;

identifying and obtaining the power spectral density of the pulsating thrust of the solid rocket engine according to the acceleration of the time domain tau and the Fourier transform of the random function of the time domain tau; and

and calculating the pulsating thrust of the solid rocket engine according to the power spectral density.

2. The method for identifying pulsating thrust of a solid rocket engine as recited in claim 1, wherein said converting acceleration in time domain t into acceleration in time domain τ yields acceleration in time domain τ, said solid rocket engine having a time-invariant characteristic in time domain τ, specifically comprising:

according to the formulaConverting the acceleration of the time domain t into the acceleration of the time domain tau; and

according to the formulaThe acceleration corresponding to the time domain tau is calculated,

wherein, the preset time period is T is more than or equal to T and less than or equal to 0, T represents the starting time, T is less than 0, and the time period corresponding to the time domain tau isr represents the rate of change of mass of the solid rocket motor,represents the acceleration of said time domain t,representing the speed of the solid rocket engine in the time domain t,according to the formulaThe calculation results in that,representing the acceleration corresponding to the time domain tau.

3. The method for identifying thrust pulsation of a solid rocket engine according to claim 2, wherein before said fourier transforming the acceleration of the time domain τ and the stochastic function of the time domain τ, respectively, said method further comprises:

time period according to the corresponding time domain tauDividing the time period into n sections, and recording the ith section as

Wherein, i represents a constant,indicates a starting value of the i-th segment,indicating the termination value of the ith segment.

4. The method for identifying the thrust pulsation of a solid rocket engine according to claim 3, wherein said fourier transforming the acceleration of the time domain τ and the random function of the time domain τ to obtain fourier transforms of the acceleration of the time domain τ and the random function of the time domain τ comprises:

fourier transformation is respectively carried out on the acceleration of the time domain tau and the random function of the time domain tau according to the following discrete Fourier transformation formula with unequal time intervals, and the Fourier transformation of the acceleration of the time domain tau and the random function of the time domain tau is obtained:

wherein,indicating that the function z (τ) is in the ith segmentA Fourier transform of the upper, N representing a positive integer greater than 1, k representing a constant,representing function at discrete pointsThe value of (a) is as follows,the discrete points are represented as a series of discrete points,representing the fourier transform factor.

5. The method for identifying pulsating thrust of a solid rocket engine as recited in claim 4, wherein a power spectral density of the pulsating thrust of the solid rocket engine is identified from the results of Fourier transformation of the acceleration of the time domain τ and the stochastic function of the time domain τ by:

wherein, representing the acceleration of said time domain tauIn the i-th stageThe result of the fourier transform on top of it,a random function g (τ) representing said time domain τ in the ith segmentThe result of Fourier transform of (c), n represents a positive integer, A (ω) represents an intermediate parameter, m₀Representing the mass of the solid rocket engine at the start time, P_fA power spectral density that represents the pulsating thrust,